Circular migrations are the periodic movement of individuals betweenmultiple locations, observed in parts of sub-SaharanAfrica. Relationships between circular migrations and HIV are complex,entailing interactions between migration frequency, partnershipstructure, and exposure to acute HIV infection. Mathematical modelingis a useful tool for understanding these interactions. Two modeling classes have dominated the HIV epidemiology and policyliterature for the last decade: one a form of compartmental models,the other network models. We construct models from each class, usingordinary differential equations and exponential random graph models,respectively. Our analysis suggests that projected HIV prevalence is highlysensitive to the choice of modeling framework. Assuming initial equalHIV prevalence across locations, compartmental models show noassociation between migration frequency and HIV prevalence orincidence, while network models show that migrations at frequenciesshorter than the acute HIV period predict greater HIV incidence andprevalence compared to longer migration periods. These differences arestatistically significant when network models are extended toincorporate a requirement for migrant men's multiple partnerships tooccur in different locations. In settings with circular migrations,commonly-used forms of compartmental models appear to miss keycomponents of HIV epidemiology stemming from interactions ofrelational and viral dynamics.